The objectives of the proposed research are the development and application of a technique for quantitative measurements of the structure of high Reynolds number gaseous shear flows. The extent of mixing at the molecular as well as the macroscopic level in shear flows will be measured instantaneously by using two different lasers and two different cameras to excite and then detect LIF from NO and acetone simultaneously. Quantitative measure ments of molecular mixing are of tremendous importance, particularly in chemically reacting systems where mixing of the fuel and oxidant streams at the molecular level is required to initiate the reactions.

Numerical and analytical models for prediction of diffusive interface growth-erosion characteristics are being formulated. The numerical model is a modal-based model for detailed simulation of convective processes. A thermal burst approach is being used for the analytical model. This model will result in a relatively simple, explicit relation for growth-erosion prediction.

Flow internal and external to nearly spherical or deformed drops and bubbles is important in many applications. In some, wall effects are important, including bubble flow through through-holes during plating of printed circuit boards. We are using a Galerkin finite-element method to computationally study steady axisymmetric flow in and around deformable drops moving along the axis of a vertical tube at intermediate Reynolds numbers (0 <= Re <= 600). We find much more deformation, and, in particular, development of considerably more nonconvexity, than in previous calculations. Future work will examine transient heat and mass transfer to deformable drops.

Construction of low-dimensional nonlinear ordinary differential equation models from measurements has been demonstrated for several incompressible flows. Although widely applicable in principle, this method has only been applied to fully-developed statistically stationary channel flows, for which its massive data requirements are met by existing data bases. We are developing a technique that uses M measured time series to construct an N > M -dimensional quadratically nonlinear (appropriate to Navier-Stokes) dynamical model. This procedure will be very attractive for free-surface flows, in which use of physically faithful models in real-time applications is precluded by complexity.

``Freckling'' and other compositional nonuniformities in directionally solidified alloys are a major concern in production of single-crystal turbine blades and other high-strength components, as well as certain electrooptic materials (e.g., mercury cadmium telluride). These macrosegregation effects have been related to a morphological instability and buoyancy-driven convection in the melt adjacent to the growing interface. We are studying uniform rigid-body rotation as a means of suppressing convection in the plane-front solidification of binary and quasi-binary alloys. We will also investigate, when the planar interface is unstable, the effect of rotation on reducing the amplitude of the motion and the resulting compositional fluctuations.

Rapid and uniform deposition of copper on the inner surface of high aspect ratio ``through-holes'' of printed circuit boards is important in electronics manufacture. We are investigating a new approach using a rotating screw electrode (RSE) inside the hole. In addition to improv- ing the electric field distribution, the RSE generates a 3-D flow that greatly enhances mass transfer. Experiments at UCLA show that plating uniformity is excellent. In the theoretical work (at Illinois), we consider the Navier-Stokes equations for the time-dependent flow between the RSE and the through-hole wall. For high aspect ratio holes, we have transformed the equations into a rotating helical coordinate system, rendering the computational problem 2-D and steady.

Unsteady 2-D flow generated by a circular cylinder started into rotatory and rectilinear motion is studied by integration of the Navier-Stokes equations, for Reynolds number 200 and several angular/rectilinear speed ratios h. For h <= 1, computation to larger dimensionless times than considered in earlier experiments and computations allows for better understanding of vortex shedding. Shedding occurs for h = 3.25 (and probably for larger h ), contrary to earlier conclusions, and differs qualitatively from the h = 0 Kármán vortex sheet. Vortices of one sense can be shed consecutively from one side, unlike the nonrotating case, in which vortices of opposite sense are shed alternately from opposite sides. Feedback control of vortex shedding is being studied using this code.

At low Reynolds numbers (Re), flow past axisymmetric bodies is steady, axisymmetric, and attached. For bluff bodies (e.g., spheres, raindrops, torpedoes), the flow separates as Re increases; ultimately, transition to unsteady, nonaxisymmetric flow occurs. We have studied this transition computationally for a fixed sphere; the steady, axisymmetric flow becomes un stable with respect to an oscillatory helical instability at Re = 175.1. The critical Re and predicted Strouhal number (dimensionless frequency) agree well with previous experiment. We are extending this work to the case where the body falls or rises freely under the action of gravity. In that case, the rigid body motion can couple to the flow disturbances, leading to a lower critical Re.

Attempts are being made to develop a parallel spectrally accurate numerical method for conducting DNS of wakes of rectangular bluff bodies. A spectral domain decomposition technique has been developed and validated in simple geometries. The method has been implemented on the massively parallel computer, CM-5.

A study to develop numerical algorithms for conducting LES of wake flows on a massively parallel computer (CM-5) is in progress. The objective is to develop parallel algorithms for unsteady flow simulations on curvilinear grids. Computer programs have been developed for both MIMD and SIMD architectures and have been validated.

A novel multigrid calculation procedure is being developed for viscous internal flows in complex geometries discretized by triangular grids. The algorithm uses a sequential update of pressures and velocities and accelerates the convergence using a FAS-FMG strategy. Calculations have been performed for flows in driven cavities of rectangular, triangular, and semicircular cross sections.

The simplest way to extract the energy from a fusion reactor is to pump liquid lithium through a ``blanket'' surrounding the fusing plasma. The design objectives are to minimize the pressure drop for the lithium flow through the strong magnetic field in the reactor and to optimize the heat transfer to the flowing lithium. Models are being developed for the three-dimensional liquid-lithium flows through various parts of the electrically insulated ducts of a design blanket for a future experimental reactor.

Ultrahigh-current motors and generators can exceed the efficiency of gears for speed reduction and can provide far greater flexibility. Electric current must flow between fixed and rotating copper surfaces, and conventional brushes cannot carry the enormous electric currents. The optimal solution appears to be a liquid metal between the rotating and fixed copper surfaces, because some liquid metals have both small electrical resistance and small viscosity. A solid metal fiber brush is also needed to stabilize the liquid metal. Models are being developed for the deflection of the fibers in the brush.

Any crystal growth experiment in an Earth-orbiting vehicle is subjected to chaotic accelerations called g-jitters. A magnetic field can be used to suppress the melt motions driven by g-jitters in order to achieve optimal crystal properties. Models are being developed for the magnetically damped melt motions and for the associated transport of dopants which determine the electrical properties of the crystal. Model predictions will be used to design the magnet damping furnace to fly on shuttle missions beginning in 1999.

In the floating zone process, there is a zone of molten semiconductor between a melting feed rod and a growing crystal. The thermocapillary convection is driven by the change of the temperature-dependent surface tension along the free surface of the floating zone. Floating zone crystal growth in space is very promising, but it is currently limited by an instability in the thermocapillary flow, leading to an oscillatory flow with adverse effects on the crystal. A magnetic field can be used to stabilize the flow and to eliminate the adverse effects of the oscillatory flow. Models are being developed to guide the selection of the optimal magnetic field.